What are the achievements of logic? It would seem to be hard to identify them.

In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.

But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.

'Socrates is mortal' and 'It is raining' - two classical conclusions of logic, can hardly be claimed as achievements.

Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal self-consistency.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

Math is math and logic is logic for very good reasons. They really do not go together. Numbers for math and relations of language for logic.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

Math is math and logic is logic for very good reasons. They really do not go together. Numbers for math and relations of language for logic.

Actually, Necromancer, Alan1000 is right. All math reduced to logic and shown that it's nothing but, has been written in a book called "Principia Mathematika", by some smart dude. He said after finishing the tome, that he got forever exhausted... he felt lethargic for the rest of his natural life, he got so much of his brain and mental work put into it.

And then some schmucks come around and declare that they don't know it, so it does not exist.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

Algebra specifically if I remember correctly, but your point rings true in some facet of memory.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

On the contrary, they failed to do this. There were always paradoxes that could not be incorporated. Later, Gödel's incompleteness theorems showed why this would always be the case.

You haven't heard that all of mathematics is reducible to logic? I'm not in a position to argue the case, but I understood that this had been achieved by about the beginning of the 20th C, due to the efforts of Russell, Frege, Whitehead et al.

I'm curious as to where you're getting your information. Of course this statement is wrong as already noted. Gödel's incompleteness theorems show that mathematical truth can not be reduced to logic.

But I saw your post on infinity over on that other site and virtually everything you say is laughably incorrect. You're just getting bad information and misunderstanding even that.

What are the achievements of logic? It would seem to be hard to identify them.

In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.

But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.

'Socrates is mortal' and 'It is raining' - two classical conclusions of logic, can hardly be claimed as achievements.

Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal self-consistency.

Does philosophy need this form of logic? If so what for?

Does anyone have any suggestions?

Incompleteness does look like the last word in this; if you can't calculate everything then all calculations are necessarily relative to initial assumptions rather than an absolute. Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).

Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).

Who believes nonsense like that? You're not known for posting silliness. Where did this come from?

Turing proved in 1936 that there are easily stated problems that no computation can solve. This result is essentially the same as Gödelian incompleteness.

Pressure in the center would form a planetary core? WTF? That's really out of left field, extremely bizarre remark. I only say this because it's unexpected from you.

Interestingly, if one attempted to construct a supercomputer capable of calculating everything, it's believed that the computer would become so large that the pressure in the centre would form a planetary core - perhaps not ideal for computing (never mind heat frying components long before that).

Who believes nonsense like that? You're not known for posting silliness. Where did this come from?

Turing proved in 1936 that there are easily stated problems that no computation can solve. This result is essentially the same as Gödelian incompleteness.

Pressure in the center would form a planetary core? WTF? That's really out of left field, extremely bizarre remark. I only say this because it's unexpected from you.

It was a curio for entertainment's sake. I was just agreeing with you otherwise.

I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole. I just extrapolated that heat etc would stymie the machine long before collapse into a black hole.

I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole.

Oh my. He was misinformed or not being serious. We already know of problems computers can't solve. Turing showed that. Building a larger computer wouldn't help in the least. This is well known but evidently not to this person on tv. Perhaps he was trying to make a point in a popularized way.

I can't find it now but the idea came from a mathematician interviewed on Through the Wormhole who had done calculations that left him with the postulation that it's impossible to know everything because, if a computer that was supposed to calculate everything was created, as it grew it would eventually collapse under its own weight to form a black hole.

Oh my. He was misinformed or not being serious. We already know of problems computers can't solve. Turing showed that. Building a larger computer wouldn't help in the least. This is well known but evidently not to this person on tv. Perhaps he was trying to make a point in a popularized way.

The theme of the show was generally about the problems with knowing everything. A variety of thinkers were interviewed, each taking a different angle. They'd already been through Gödel's incompleteness theorems and other less colourful perspectives, and I think the idea was basically that, even if all other factors were not present, it is not even physically possible to calculate everything. Basically, it was the final kicker for any doubters who may have found other approaches too heady or confusing to be convincing.

Thanks for saying I'm sane - I probably just seem so by philosophy forum standards